Vallesi et al. (2005) studied the Simon effect among 10 volunteers. The Simon effect is a phenomenon in which people’s reaction time to stimuli is faster when the stimulus is on the same side as the reaction mechanism. For example, when a light flashes on our right side (the stimulus), our reaction time is shorter when the button we are to push is also on our right instead of on our left. The authors wish to know whether the Simon effect exists and is of the same magnitude when the orientation is vertical (up/down) rather than horizontal (left/right). Because people are highly variable in their reaction times, and because it is expensive to recruit and process participants, it makes sense to use people as blocks; that is, to use a repeated measures design.
Each volunteer was tested in all four combinations of two possible Task orientations (horizontal/vertical) and two possible Correspondence configurations (corresponding/ noncorresponding). The dependent variable was reaction time in milliseconds. The authors describe this as a “2
2 within subject experiment.” The hypothesis of major interest is whether or not there will be an interaction; that is, whether the size of the discrepancy between corresponding and noncorresponding orientations will differ when the Task is vertical rather than horizontal.
The graphical and tabular summary of the results are important in understanding the results, and they are similar to what would be produced if this were a 2
2 CRD. The means within each cell are as follows:
These can be converted to a profile plot. Examining the plot suggests that the Simon effect is of about the same magnitude in both orientations; that is, that the interaction is at most quite weak.
The results of the repeated measures ANOVA are consistent with the plot. The authors state:
The two main effects were significant ½F(1; 9) = 41:3, P
:001 for correspondence, and F(1; 9) = 8:2; P
:05 for task] .... No significant interaction was found.
Note that the degrees of freedom for these tests are substantially smaller than for a CRD with Subject, Correspondence, and Task as factors and the Subject interactions pooled to estimate error. That is because, under the repeated measures blocking structure, the denominator for the F test for Correspondence uses the Correspondence
Subject interaction (see Table 10.16). This term has 9
1 degrees of freedom. Similarly, the F test for Task uses the Task
Subject interaction in the denominator.